Some results on random design regression with long memory errors and predictors

Details Some results on random design regression with long memory errors and predictors Some results on random design regression with long memory errors and predictors

2011-02-21

arxiv.org/abs/1102.4372v1

Journal of Statistical Planning and Inference, 141, 508--523, 2011

Mathematics

Statistics Theory

Scientific paper

This paper studies nonparametric regression with long memory (LRD) errors and predictors. First, we formulate general conditions which guarantee the standard rate of convergence for a nonparametric kernel estimator. Second, we calculate the Mean Integrated Squared Error (MISE). In particular, we show that LRD of errors may influence MISE. On the other hand, an estimator for a shape function is typically not influenced by LRD in errors. Finally, we investigate properties of a data-driven bandwidth choice. We show that Averaged Squared Error (ASE) is a good approximation of MISE, however, this is not the case for a cross-validation criterion.

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